Question

the dissociation of a weak electrolyte is suppressed when
a strong electrolyte with a common ion is added to the weak electrolyte solution.
a strong salt is dissolved with the weak electrolyte solution.
a strong electrolyte with a different ion than the weak electrolyte is added.
the strong electrolyte solidifies in the presence of the weak electrolyte.

Explanation:

This is based on the common - ion effect. The common - ion effect states that when a strong electrolyte containing an ion common to the ions of a weak electrolyte is added to a solution of the weak electrolyte, the dissociation of the weak electrolyte is suppressed. For example, if we have a weak electrolyte like acetic acid ($\ce{CH_3COOH}$) which dissociates as $\ce{CH_3COOH
ightleftharpoons CH_3COO^- + H^+}$, and we add a strong electrolyte like sodium acetate ($\ce{CH_3COONa}$) which provides $\ce{CH_3COO^-}$ ions (a common ion), the equilibrium shifts to the left, suppressing the dissociation of acetic acid. The other options do not relate to the principle of suppressing the dissociation of a weak electrolyte: dissolving a strong salt without a common ion (second option) or with a different ion (third option) does not suppress the weak electrolyte's dissociation, and the solidification of a strong electrolyte (fourth option) has no relation to the dissociation of a weak electrolyte.

Answer:

a strong electrolyte with a common ion is added to the weak electrolyte solution.